KURT Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is a verified release, not a final supported version.
• Scope: Desktop Calc, English function names and semicolon-separated formulas. Locale and file-format mappings may differ.
• Checked: October 14, 2026. Eight reference formulas and the listed boundary cases were recalculated in 4.1.16 on Linux x86-64, Build 9816, using XLSX import. Source and independent mathematics were also checked.

KURT returns a finite-sample-adjusted excess-kurtosis statistic based on the fourth standardized central moment. “Excess” means the reference normal-distribution kurtosis of 3 has been accounted for. It is not the unadjusted fourth moment and not a test that a sample is normally distributed. Release implementation.

=KURT(Number1 [; Number2; …])

Supply numeric observations as arguments or ranges. The stated sample formula requires at least four observations and nonzero sample variance. The collector reads numeric cells from referenced ranges. Constant observations and undersized samples have no valid value under this formula; the displayed native diagnostics below retain their actual errors.

These eight formulas were recalculated in the stated 4.1.16 build using XLSX import. Saved numeric results agree with independent high-precision calculations; values below are rounded to twelve decimal places. The comparison concerns stored values, not a claim that every display format prints the same digits.

For the range formulas, enter these values in the indicated columns and rows. Keep labels outside the calculation ranges.

For 1, 2, 3 and 4, =KURT(1;2;3;4) returns −1.2. A negative result is valid excess kurtosis, not an error. The uniform A column from 1 through 10 also gives −1.2.

The B column replaces the last value 10 with 100. Its fourth-power contribution sharply increases kurtosis. The E column reverses every B value’s sign, but KURT remains unchanged because fourth powers do not distinguish the direction of the tail. Keep an actual distribution plot or the observations alongside this single summary.

Let n be the count, x̄ the sample mean and s the sample standard deviation with denominator n−1. The implemented statistic is n(n+1)Σ((x−x̄)/s)^4/((n−1)(n−2)(n−3)) − 3(n−1)^2/((n−2)(n−3)). Using a population standard deviation in that expression gives a different result.

For 1,2,3,4 the centered squared sum is 5, so s²=5/3; substituting into the formula gives −1.2. Multiplying all observations by a nonzero constant or adding a constant does not change the exact statistic. Those invariances explain the scaled and reflected examples.

High sample excess kurtosis is often driven by extreme observations relative to overall spread. It should not be described solely as “a sharper peak,” nor used alone to establish a particular tail model or distributional family.

Kurtosis can be unstable in small samples and sensitive to individual outliers. A finite result does not establish that the population has a finite fourth moment or that the sampling assumptions are appropriate. Investigate data quality rather than automatically removing an observation because it raises kurtosis.

The source explicitly checks zero spread and uses denominators involving n−2 and n−3. Do not replace an undefined statistic with zero: zero would mean a particular excess-kurtosis value, not missing or invalid evidence.

The following boundary formulas were recalculated in the same named method. H5 and H6 are deliberately empty cells where referenced. An error display remains an error even if the underlying ODS numeric attribute stores zero.

• stdev
• var
• average

• Function-specific release entry
• Numeric helper or argument collection

The retained input and saved ODS preserve the tested formula identities. A stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence is limited to the eight reference formulas and listed boundary cases in this exact release and method. Composite explanatory examples are independent calculations unless listed among those cases; other releases, locales and extreme-parameter accuracy were not established.